The wavelength dependence of the group velocity of light propagating in an optical fiber leads to pulse distortion. Wavelength-dependent pulse distortion is commonly called group chromatic dispersion (CD) and can lead to high bit error rates or even signal loss if left uncorrected. The problem becomes particularly severe at high data rates and over long transmission distances. In the conventional approach to CD correction, a pulse is detected after a short transmission distance, reshaped in the electronic domain, and retransmitted. For Dense Wave Division Multiplexing (DWDM) systems, reshaping in the electronic domain is too costly.
It is known that CD can be corrected in the optical domain using a dispersion compensator which provides compensating dispersion. For example, a Gires-Tournois etalon (GTE) can provide periodic compensating dispersion at frequencies aligned to the International Telecommunications Union (ITU) transmission channel grids.
A GTE consists of a partially reflecting mirror at the input face and a totally reflecting mirror at the rear. These two mirrors are parallel and separated by a distance in between. As a result of the cavity between the mirrors, the wavelength-dependent phase shift a beam experiences upon interaction with a GTE can be written                     ϕ        =                  2          ⁢                                          ⁢                                    tan                              -                1                                      ⁡                          (                                                                    1                    +                                          R                                                                            1                    -                                          R                                                                      ⁢                                  tan                  ⁡                                      (                                                                  ω                        c                                            ⁢                      n                      ⁢                                                                                          ⁢                      d                                        )                                                              )                                                          (        1        )            where R is the mirror reflectivity of the front mirror, n is the index of refraction of the cavity medium and d is the space between the mirrors. Notice that the phase shift depends on the frequency of light ω.
The compensating group delay can be obtained by taking a derivative of the phase shift with respect to the frequency ω. This leads to                                           τ            =                                                            ⅆ                  ϕ                                                  ⅆ                  ω                                            =                                                σ                                      1                    +                                                                  (                                                                              σ                            2                                                    -                          1                                                )                                            ⁢                                                                        sin                          2                                                ⁡                                                  (                                                      ω                            ⁢                                                                                                                  ⁢                            n                            ⁢                                                                                                                  ⁢                                                          d                              /                              c                                                                                )                                                                                                                    ⁢                                  τ                  0                                                              ⁢                                          ⁢          where                ⁢                                                      (        2        )                                                          ⁢                              σ            =                                          1                +                                  R                                                            1                -                                  R                                                              ⁢                                          ⁢          and                                    (        3        )                                                          ⁢                              τ            0                    =                                                                      ⅆ                                                                                                          ⅆ                  ω                                            ⁢                              (                                  2                  ⁢                                      ω                    c                                    ⁢                  n                  ⁢                                                                          ⁢                  d                                )                                      =                                          2                ⁢                d                                            v                g                                                                        (        4        )            Here, τ0 is the round trip flight time inside the cavity; vg is the group velocity of light inside the cavity medium. For a vacuum cavity, vg is c, for a non-vacuum cavity, vg is c/n.
The compensating CD (in units of ps/nm) is defined as the derivative of the group delay Γ with respect to wavelength λ, that is                     CD        =                                            ⅆ              τ                                      ⅆ              λ                                =                                    -                                                2                  ⁢                                                                          ⁢                  π                  ⁢                                                                          ⁢                  c                                                  λ                  2                                                      ⁢                                          ⅆ                τ                                            ⅆ                ω                                                                        (        5        )            
The amount of compensating dispersion provided by a single GTE interaction has generally been inadequate for long distance broadband applications. Multiple GTE arrangements—for example, dual GTEs separated by a zig-zag beam path—have achieved a higher amount of compensating dispersion. However, known multiple GTE arrangements have experienced problems of beam walk-off due to the oblique incidence of the beam's arrival at the GTEs. As well, multiple GTE interactions are needed in order to increase the bandwidth of the periodic CD function required for CD compensation.
In summary, to adequately correct CD in long distance, broadband applications, multiple GTE interactions are needed. However, to avoid beam walk-off, the beam must arrive at substantially normal incidence for each of the multiple GTE interactions.